question_answer

An explosion blows a rock into three parts. Two parts go off at right angles of each other. These two are 1 kg first part moving with a velocity of \[12\,m{{s}^{-1}}\] and 2 kg second part moving with a velocity of  \[8\,m{{s}^{-1}}\]. If the third part files off with a velocity of \[4\,m{{s}^{-1}},\] its mass would be :

A) 5 kg

B) 7 kg           

C) 17 kg

D) 3 kg

Correct Answer: A

Solution :

[a] Apply law of conservation of linear momentum. Momentum of first part \[=1\times 12=12\,kg\,m{{s}^{-1}}\]. Momentum of the second part \[=2\times 8=16\,kg\,m{{s}^{-1}}\].  Resultant momentum \[=\sqrt{{{(12)}^{2}}+{{(16)}^{2}}}=20\,kg\,m{{s}^{-1}}\]. The third part should also have the same momentum. Let the mass of the third part be M, then \[4\times M=20\Rightarrow M=5\,kg\]